Please excuse this extemly low intelliegent question but I'm only in high school and therefore don't know the answer nor how to google it. It is, what is the difference between college Algebra and the two levels of Algebra learned in high school? Thanks.
It depends on what you mean by college algebra. The class taught to freshman is aimed at the people who should have learned algebra in high school. If you have done well in your high school algebra classes you will not need to take a remedial college class. The vast majority of incoming freshman who plan to get a degree in math, science, or engineering take calculus. To major in mathematics you do need to take a class in algebra. In fact, math majors take several courses in algebra. These classes are anything but remedial algebra; the remedial courses do not count as math courses toward a degree in mathematics. Calculus and analysis are prerequisites for this kind of algebra course.
Just to give an idea of what algebra is like at the graduate level. http://books.google.com/books?id=1AZfvv-Ava0C (spelling fixed): Graduate algebra: commutative view By Louis Halle Rowen This book is an expanded text for a graduate course in commutative algebra, focusing on the algebraic underpinnings of algebraic geometry and of number theory. Accordingly, the theory of affine algebras is featured, treated both directly and via the theory of Noetherian and Artinian modules, and the theory of graded algebras is included to provide the foundation for projective varieties. Major topics include the theory of modules over a principal ideal domain, and its applications to matrix theory (including the Jordan decomposition), the Galois theory of field extensions, transcendence degree, the prime spectrum of an algebra, localization, and the classical theory of Noetherian and Artinian rings. Later chapters include some algebraic theory of elliptic curves (featuring the Mordell-Weil theorem) and valuation theory, including local fields. One feature of the book is an extension of the text through a series of appendices. This permits the inclusion of more advanced material, such as transcendental field extensions, the discriminant and resultant, the theory of Dedekind domains, and basic theorems of rings of algebraic integers. An extended appendix on derivations includes the Jacobian conjecture and Makar-Limanov's theory of locally nilpotent derivations. Grobner bases can be found in another appendix. Exercises provide a further extension of the text. The book can be used both as a textbook and as a reference source. This site, http://www.math.uiuc.edu/~r-ash/Algebra.html, contains the text (pdf format) for a first graduate level course in abstract algebra. In short, what you are taught as algebra in high school is nothing like the subject with the same name as taught to mathematicians.
oh ya I can tell by terms on top of the fact that in the Algebra I learned and am learning there was and are no theories. It's all straight forward. Thanks for the bottum link. Please Register or Log in to view the hidden image!
In my mind, when I hear ``college algebra'', it just means ``take both high school algebra courses and combine them in a one year course''. Of course, as DH pointed out, it depends on the context. ``Algebra'' has a very broad meaning. If the course is part of your freshman curriculum, or if you aren't a math major, this is probably what it means.
